Vinayaka Missions University 2010 B.E Mechanical Engineering Maths - Question Paper
B.E. DEGREE EXAMINATION Third Semester
SLNo.E7690D
MECHANICAL ENGINEERING
l ime: Three hours Maximum: 80 marks
Answer ALL questions
1. A is known to hit the target in 2 out of 5 shots where as B is known as the target in 3 out of 4 shots. Find the probability of the target being hit when they both try?
2. Suppose that the random variable X assumes three values 0.1 and 2 with probabilities 1/3. 1/6. 'A respectively, obtain the distribution function of X.
3. If the probability that a target is destroyed on any one shot is 0.5, what is the probability that it would be destroyed on 6th attempt?
4. Find the binomial distribution for which the mean is 4 and variance is 3.
5. Find the acute angle between the tw'o lines of regression.
'v Prove that r = Jbxybvx .
~!. Define null hypothesis and alternative hypothesis.
8. Mention any two conditions for using a-2 test.
9. Write down the Hasic steps in ANOVA.
10. Write dowrn the format of ANOVA table for One-Way classification.
if. a) (i) An urn contains 5 balls. Two balls are drawn and are found to be white the probability of all the balls being white?
. What is (6) (6)
(ii) State and prove Baye's theorem.
b) Find the moment generating function of random variable with probability law P(X = *) - qx~'p,x = 1,2.3.... Find the mean and variance.
12. a) (i) Find mean and variance of geometric distribution. (6)
(ii) A die is cast until 6 appears. What is the probability that it must be cast more than five times? (6)
OR
b) (i) Find the mean and variance of uniform distribution. (6)
(ii) A random variable X has a uniform distribution over (-3,3), compute.
(i) P( X < 2) (ii) P(!Xj < 2), P(|X -2j < 2). (6)
(p.t.o)
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